The topology of a power grid affects its dynamic operation and settlement in the electricity market. Real-time topology identification can enable faster control action following an emergency scenario like failure of a line. This article discusses a graphical model framework for topology estimation in bulk power grids (both loopy transmission and radial distribution) using measurements of voltage collected from the grid nodes. The graphical model for the probability distribution of nodal voltages in linear power flow models is shown to include additional edges along with the operational edges in the true grid. Our proposed estimation algorithms first learn the graphical model and subsequently extract the operational edges using either thresholding or a neighborhood counting scheme. For grid topologies containing no three-node cycles (two buses do not share a common neighbor), we prove that an exact extraction of the operational topology is theoretically guaranteed. This includes a majority of distribution grids that have radial topologies. For grids that include cycles of length three, we provide sufficient conditions that ensure existence of algorithms for exact reconstruction. In particular, for grids with constant impedance per unit length and uniform injection covariances, this observation leads to conditions on geographical placement of the buses. The performance of algorithms is demonstrated in test case simulations.
We consider the problem of recovering off-the-grid spikes from Fourier measurements. Successful methods such as sliding Frank-Wolfe and continuous orthogonal matching pursuit (OMP) iteratively add spikes to the solution then perform a costly (when the number of spikes is large) descent on all parameters at each iteration. In 2D, it was shown that performing a projected gradient descent (PGD) from a gridded over-parametrized initialization was faster than continuous orthogonal matching pursuit. In this paper, we propose an off-the-grid over-parametrized initialization of the PGD based on OMP th…
We present a method for joint phase identification and topology recovery in unbalanced three phase radial networks using only voltage measurements. By recovering phases and topology jointly, we utilize all three phase voltage measurements and can handle networks where some buses have a subset of three phases. Our method is theoretically justified by a novel linearized formulation of unbalanced three phase power flow and makes precisely defined and reasonable assumptions on line impedances and load statistics. We validate our method on three IEEE test networks simulated under realistic conditio…
Voltage control generally requires accurate information about the grid's topology in order to guarantee network stability. However, accurate topology identification is a challenging problem for existing methods, especially as the grid is subject to increasingly frequent reconfiguration due to the adoption of renewable energy. Further, running existing control mechanisms with incorrect network information may lead to unstable control. In this work, we combine a nested convex body chasing algorithm with a robust predictive controller to achieve provably finite-time convergence to safe voltage li…
This letter addresses the estimation of directions-of-arrival (DoA) by a sensor array using a sparse model in the presence of array calibration errors and off-grid directions. The received signal utilizes previously used models for unknown errors in calibration and structured linear representation of the off-grid effect. A convex optimization problem is formulated with an objective function to promote two-layer joint block-sparsity with its second-order cone programming (SOCP) representation. The performance of the proposed method is demonstrated by numerical simulations and compared with the …
Operators can now remotely control switches and update the control settings for voltage regulators and distributed energy resources (DERs), thus unleashing the network reconfiguration opportunities to improve efficiency. Aligned to this direction, this work puts forth a comprehensive toolbox of optimization models leveraging the control capabilities of smart grid assets. We put forth detailed yet practical models to capture the operation of locally and remotely controlled regulators, and customize the watt-var DER control curves complying with the IEEE 1547.8 mandates. Maintaining radiality is…
University of Minnesota（明尼苏达大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 minutes. Granted the grid Laplacian is a parameter of this LP, one could infer such a topology-revealing matrix upon observin…
Wide-area dynamic studies are of paramount importance to ensure the stability and reliability of power grids. The rising deployment synchrophasor and other sensing technologies has made data-driven modeling and analysis possible using the synchronized fast-rate dynamic measurements. This paper presents a general model-free framework of inferring the grid dynamic responses using the ubiquitous ambient data collected during normal grid operations. Building upon the second-order dynamic model, we have established the connection from the cross-correlation of various types of angle, frequency, and …
Estimation of the operational topology of the power grid is necessary for optimal market settlement and reliable dynamic operation of the grid. This paper presents a novel framework for topology estimation for general power grids (loopy or radial) using time-series measurements of nodal voltage phase angles that arise from the swing dynamics. Our learning framework utilizes multivariate Wiener filtering to unravel the interaction between fluctuations in voltage angles at different nodes and identifies operational edges by considering the phase response of the elements of the multivariate Wiene…
Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of smart inverters, we have previously advocated perturbing their power injections to unveil the underlying grid topology using the induced voltage responses. Under an approximate grid model, the perturbed power injections and the collected voltage deviations obey a linear regression setup, where the unknown is the vector of line resistances. Building on this m…
Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages o…
Knowing the connectivity and line parameters of the underlying electric distribution network is a prerequisite for solving any grid optimization task. Although distribution grids lack observability and comprehensive metering, inverters with advanced cyber capabilities currently interface solar panels and energy storage devices to the grid. Smart inverters have been widely used for grid control and optimization, yet the fresh idea here is to engage them towards network topology inference. Being an electric circuit, a distribution grid can be intentionally probed by instantaneously perturbing in…
To perform any meaningful optimization task, power distribution operators need to know the topology and line impedances of their electric networks. Nevertheless, distribution grids currently lack a comprehensive metering infrastructure. Although smart inverters are widely used for control purposes, they have been recently advocated as the means for an active data acquisition paradigm: Reading the voltage deviations induced by intentionally perturbing inverter injections, the system operator can potentially recover the electric grid topology. Adopting inverter probing for feeder processing, a s…
Operations of substation circuit breakers are important for maintenance needs and topology reconfiguration in power systems. Bus splitting is one type of topology change where the two bus bars at a substation can become electrically disconnected under certain actions of circuit breakers. Because these events involve detailed substation modeling, they are typically not considered in routine power system operation and control. In this paper, an improved substation-level topology optimization framework is developed by expanding traditional line switching decisions by breaker-level bus splitting, …
A coordinated cyber-attack on grid meter readings and breaker statuses can lead to incorrect state estimation that can subsequently destabilize the grid. This paper studies cyber-attacks by an adversary that changes breaker statuses on transmission lines to affect the estimation of the grid topology. The adversary, however, is incapable of changing the value of any meter data and can only block recorded measurements on certain lines from being transmitted to the control center. The proposed framework, with limited resource requirements as compared to standard data attacks, thus extends the sco…
The dynamic response of power grids to small disturbances influences their overall stability. This paper examines the effect of network topology on the linearized time-invariant dynamics of electric power systems. The proposed framework utilizes ${\cal H}_2$-norm based stability metrics to study the optimal placement of lines on existing networks as well as the topology design of new networks. The design task is first posed as an NP-hard mixed-integer nonlinear program (MINLP) that is exactly reformulated as a mixed-integer linear program (MILP) using McCormick linearization. To improve comput…
Power distribution in remote communities often depends on off-grid microgrids. In order to address the reliability challenges for these microgrids, we develop a mathematical model for topology design, capacity planning, and operation of distributed energy resources in microgrids that includes N-1 security analysis. Due to the prohibitive size of the optimization problem, we develop a rolling-horizon algorithm that is combined with scenario-based decomposition to efficiently solve the model. We demonstrate the efficiency of our algorithm on an adapted IEEE test network and a real network from a…
Improved steady-state stability of power grids with a communication infrastructure
Macedonian Academy of Sciences and Arts（马其顿科学院与艺术院）；Faculty of electrical engineering and information technologies, University “Ss Cyril and Methodius”（西里尔和梅托迪乌斯大学电气工程和信息技术学院）；Faculty of Computer Sciences and Engineering, University “Ss Cyril and Methodius”（西里尔和梅托迪乌斯大学计算机科学与工程系）；BioCircuits Institute, UC San Diego（加州大学圣地亚哥分校生物电路研究所）
Distribution grids constitute complex networks of lines often times reconfigured to minimize losses, balance loads, alleviate faults, or for maintenance purposes. Topology monitoring becomes a critical task for optimal grid scheduling. While synchrophasor installations are limited in low-voltage grids, utilities have an abundance of smart meter data at their disposal. In this context, a statistical learning framework is put forth for verifying single-phase grid structures using non-synchronized voltage data. The related maximum likelihood task boils down to minimizing a non-convex function ove…
This paper presents a novel modified Viterbi algorithm to identify the optimal distribution system restoration plan for improving the grid resiliency. In the proposed algorithm, the switching operations performed for system restoration are the states with the minimum bus voltage being seen as the cost metric for each state and the extent of load recovery as the observed event. When full load recovery is spotted, the dynamic programming algorithm stops, thereby giving the least number of switching pairs necessary for system restoration. Moreover, an improved flexible switching pair operation is…
The dynamic response of power grids to small transient events or persistent stochastic disturbances influences their stable operation. This paper studies the effect of topology on the linear time-invariant dynamics of power networks. For a variety of stability metrics, a unified framework based on the $H_2$-norm of the system is presented. The proposed framework assesses the robustness of power grids to small disturbances and is used to study the optimal placement of new lines on existing networks as well as the design of radial (tree) and meshed (loopy) topologies for new networks. Although t…
Malicious attacks in the power system can eventually result in a large-scale cascade failure if not attended on time. These attacks, which are traditionally classified into \emph{physical} and \emph{cyber attacks}, can be avoided by using the latest and advanced detection mechanisms. However, a new threat called \emph{cyber-physical attacks} which jointly target both the physical and cyber layers of the system to interfere the operations of the power grid is more malicious as compared with the traditional attacks. In this paper, we propose a new cyber-physical attack strategy where the transmi…
